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How the Square Root of 2 Became a Number
Useful mathematical concepts, like the number line, can linger for millennia before they are rigorously defined.
The Enduring Mystery of How Water Freezes
Making ice requires more than subzero temperatures. The unpredictable process takes microscopic scaffolding, random jiggling and often a little bit of bacteria.
The S-Matrix Is the Oracle Physicists Turn To in Times of Crisis
Particle physicists in search of the next theory of reality are consulting a mathematical structure that they know will never fail: a table of possibilities known as the S-matrix.
Computer Scientists Invent an Efficient New Way to Count
By making use of randomness, a team has created a simple algorithm for estimating large numbers of distinct objects in a stream of data.
How Do Machines ‘Grok’ Data?
By apparently overtraining them, researchers have seen neural networks discover novel solutions to problems.
The Hidden Connection That Changed Number Theory
Quadratic reciprocity lurks around many corners in mathematics. By proving it, number theorists reimagined their whole field.
The Deep Link Equating Math Proofs and Computer Programs
Mathematical logic and the code of computer programs are, in an exact way, mirror images of each other.
How Many Microbes Does It Take to Make You Sick?
Exposure to a virus isn’t an all-or-nothing proposition. The concept of “infectious dose” suggests ways to keep ourselves safer from harm.
How Scientists Are Tackling the Tricky Task of Solar Cycle Prediction
Scientists have struggled to accurately forecast the strength of the sun’s 11-year cycle — even after centuries of solar observations.